Design of modified UCHT sequences

In this paper, we consider the design of a class of unified complex Hadamard transform (UCHT) sequences. An efficient modification is imposed to those sequences to better suit applications in asynchronous code-division multiple-access (CDMA) systems. These modified UCHT sequences preserve the orthogonality of the original UCHT sequences and offer increased design options due to an increased number of parameters. The design of UCHT, modified UCHT, and Oppermann sequences is then formulated with reference to optimizing the maximum nontrivial aperiodic correlation value. These optimization problems can then be solved efficiently using a genetic algorithm with the maximum nontrivial aperiodic correlation value serving in the definition of a fitness function. Numerical examples illustrate the benefits of modified UCHT sequences over the original UCHT sequences